Prove that the midpoints of an equilateral triangle form ano

Prove that the midpoints of an equilateral triangle form another equilateral triangle.

Solution

In equilateral triangle ABC, the mid-points of sides BC,CA and AB are respectively D,E and F. Prove that triangle DEF is an equilateral triangle.

Triangle ABC is an equilateral triangle.
AB = BC = AC
DE = 1/2 AB

EF = 1/2 BC
EF = 1/2 AB [Since AB = BC = AC]

DF = 1/2 AC
DF = 1/2 AB [Since AB = BC = AC]

DE = EF = DF

DEF is an equilateral triangle.